"Ghosts, ghosts... Wizards can leave an imprint of themselves in the world. Most become ghosts not because of lingering magic, but because they cannot let go of something.
"Otherwise, how could the ghost of a young student like Moaning Myrtle have existed for decades alongside the ghosts of powerful wizards?
"Wizards can choose whether to become ghosts. Those who are desperately afraid of death, or who remain fixated on something from their lives, stay behind as ghosts.
"Ghosts exist forever between life and death. It's a pitiful existence, and they can never find happiness in the world again.
"They're pitiable because they've lost certain abilities.
"They have intelligence, but it rests on their memories from life. They merely imitate how they behaved while alive. They can't even learn anything new; at most, they can refine knowledge and skills they had already learned but never mastered."
Snape explained the nature of ghosts to Will in a dry voice.
"They aren't remnants of a wizard's magic. They're more like a pitiful, deeply etched memory."
It was a convoluted explanation, but Will understood it.
In short, ghosts in this world were like artificial intelligences frozen in place. Some problem with their data had left them behind, and wizards had no idea where their back end was, so they couldn't update them. The data wandered the world as ghosts, neither growing nor diminishing. At most, it could keep checking itself.
By that logic, if Snape died in an accident right now, he would probably become a ghost too.
Ghosts didn't linger because of a wizard's magic, but because of an obsession. Or was it emotion? A spiritual imprint?
Then what was the faint magic in ghosts? Will thought of Natural Magic. Magic in this world responded to wizards' emotions and will. Perhaps ghosts had